$A$ cell sends a current through a resistance $R$ for time $t$. Now the same cell sends current through another resistance $r$ for the same time. If the same amount of heat is developed in both the resistances,then the internal resistance of the cell is:

Three identical cells,each of emf $10 \ V$ and internal resistance $3 \ \Omega$,are connected in parallel across terminals $A$ and $B$. The net emf across $A$ and $B$ is .......... $V$.

Given below are two statements $:$
Statement-$I$ : The equivalent emf of two non-ideal batteries connected in parallel is smaller than either of the two emfs.
Statement-$II$ : The equivalent internal resistance of two non-ideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries.
In the light of the above statements,choose the correct answer from the options given below.

$A$ cell of emf $10 \text{ V}$ and internal resistance $3 \Omega$ is connected in parallel with another cell of emf $7 \text{ V}$ and internal resistance $\frac{3}{5} \Omega$,such that their positive terminals are joined together and their negative terminals are joined together. Their combined positive terminal is joined with the negative terminal,and their combined negative terminal is joined with the positive terminal of a third cell of emf $20 \text{ V}$ with internal resistance $2 \Omega$. The combination can be replaced by a battery of emf $E$ and internal resistance $r$. The values of $E$ and $r$ are respectively:

$A$ battery of $24$ cells,each of emf $1.5\, V$ and internal resistance $2\, \Omega$,is to be connected to send the maximum current through a $12\, \Omega$ resistor. The correct arrangement of cells will be:

The electromotive force of a primary cell is $2\,V$. When it is short-circuited,it gives a current of $4\,A$. Its internal resistance in $\Omega$ is: